Problem: $y=x^4$ $\dfrac{dy}{dx}=$
$y$ is of the form $x^n$ and therefore we can apply the power rule: $\dfrac{d}{dx}[x^n]=n\cdot x^{n-1}$ $\begin{aligned} \dfrac{dy}{dx}&=\dfrac{d}{dx}[x^{{4}}] \\\\ &={4}x^{{4}-1} \\\\ &=4x^3 \end{aligned}$ In conclusion, $\dfrac{dy}{dx}=4x^3$